It didn't help to abort the stalled downloads, or aborting the whole task - it was STILL complaining about those downloads!!

That's a different problem. These tasks were created before the http->https transition, so they still want to download through http, but that won't succeed. You have to abort the downloads, then restart the BOINC manager, or manually edit the client_state.xml file (see the Warning: bad tasks re-appearing in the download queue thread for details).

I'm not sure that the task generated by a "repaired" task would come using https, so we may do it 10 times.
(I've aborted the transfer of these tasks, then restarted the BOINC manager, as it thinks that "some downloads are stalled". It refers to the ones I've aborted.)

I'm sure about it. I have this problem on my symmetrical 1Gbps fiber optics internet connection. Earlier I had an ADSL (through an old phone line copper wire) with 50Mbps download 15Mbps upload bandwidth, which had the same problem.

It should be set to 1 for GPUGrid, but this property is set by the GPUGrid project in the tasks (so this option has no effect on GPUGrid tasks, until it's set by the project).
Look for <report_immediately/> in the client_state.xml and you'll find similar records:

Can somebody confirm if the system works (after resetting the project)?

It's not enough to reset the project, you should remove the project from BOINC manager (detach the host), then re-add the project with https://www.gpugrid.net/ . When adding GPUGrid, you should manually type in the 's' at the end of http before the colon (':') in the 'Project URL' field of the dialog box before you click on the 'next' button.
Otherwise it's working fine.

Important: Remember to back up your app_config.xml from the project's folder before you remove the project, as this process will erase all files from this folder and remove the folder, then create the folder and download everything again from the project's servers (but that does not include the app_config.xml, which is created by the user).

Can somebody confirm if the system works (after resetting the project)?

It's not enough to reset the project, you should remove the project from BOINC manager (detach the host), then re-add the project with https://www.gpugrid.net/ . When adding GPUGrid, you should manually type in the 's' at the end of http before the colon (':') in the 'Project URL' field of the dialog box before you click on the 'next' button.
Otherwise it's working fine.

This is not a request show.
To keep your GPU busy all the time, attach your host to other GPU project(s), either within BOINC (setting zero resource share for these backup projects), or other ways (folding@home see the folding@home thead here for instructions, or quarantine@home)

It will take at least 5-10 days (or more) until all the workunits out in the field are finished (or timed out, and finished on another host).
I don't expect that another batch will be queued until then.
Exam period is coming, then the summer break is coming, so perhaps there won't be much work queued soon.
Unless Toni prepared some COVID-19 related work. Or perhaps we could help out the Acellera drug design people doing their job.